To Solve A Rational Inequality We Factor The Numerator And The Denominator Into Irreducible Factors The Cut Points Are 1 (19.31 KiB) Viewed 59 times
To solve a rational inequality, we factor the numerator and the denominator into irreducible factors. The cut points are the real ---Select--- numerator and the real ---Select--- of the denominator. Then we find the intervals determined by the ---Select-- the sign of the rational function on each interval. Let (x + 4)(x - 1) (x-7)(x + 9) Fill in the diagram below to find the intervals on which r(x) ≥ 0. Sign of -9 -4 1 X+4 x-1 x - 7 x +9 (x + 4)(x - 1) (x-7)(x + 9) From the diagram we see that r(x) > 0 on the intervals r(x) = ? ✓ ? ♥ ? Y ? ? ? V ? ♥ ? ♥ ? ✓ ? ♥ ? V 7 ? V ? V ? V (Enter your answer using interval notation.) of the and we use test points to find T
To solve a polynomial inequality, we factor the polynomial into irreducible factors and find all the real ---Select--of the polynomial. Then we find the intervals determined by the real ---Select--- and use test points in each interval to find the sign of the polynomial on that interval. Let P(x) = x(x + 5)(x - 1). Fill in the diagram below to find the intervals on which P(x) > 0. Sign of -5 1 x + 5 x-1 x(x + 5)(x - 1) ? ✓ ? ♥ ? ♥ ? ♥ ? ✓ ? ♥ ? ✓ From the diagram above we see that P(x) 20 on the intervals ? ✓ ? ♥ (Enter your answer using interval notation.)
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